Reactive, Inelastic, and Dissociation Processes in Collisions of Atomic

Subscriber access provided by Hong Kong University of Science and Technology Library

Article

Reactive, Inelastic and Dissociation Processes in Collisions of Atomic Oxygen with Molecular Nitrogen

The Journal of Physical Chemistry A is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any


Fabrizio Esposito, and Iole Armenise

J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/ acs.jpca.7b04442 • Publication Date (Web): 24 Jul 2017 Downloaded from http://pubs.acs.org on July 27, 2017



Just Accepted

“Just Accepted” manuscripts have been peer-reviewed and accepted fo online prior to technical editing, formatting for publication and author pro Society provides “Just Accepted” as a free service to the researc dissemination of scientific material as soon as possible after acceptance appear in full in PDF format accompanied by an HTML abstract. “Just Ac



fully peer reviewed, but should not be considered the official version of re readers and citable by the Digital Object Identifier (DOI®). “Just Accepte to authors. Therefore, the “Just Accepted” Web site may not include al in the journal. After a manuscript is technically edited and formatted, it Accepted” Web site and published as an ASAP article. Note that technic changes to the manuscript text and/or graphics which could affect con



and ethical guidelines that apply to the journal pertain. ACS cannot or consequences arising from the use of information contained in these


rate coefficient (cm3/s)

1.0e−10 1.0e−12

2000

3000

4000

5000

7000

The Journal of Physical Chemistry T (K)

10000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

20000

Page 1 of 24

this work Baulch (forward) Baulch (reverse) Bose and Candler extrapolation

1.0e−14 1.0e−16 1.0e−18 1.0e−20

ACS 1 Paragon 2 Plus Environment 3 4 −1

10000/T (K )

5

6

1.0e−09


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

The Journal of Physical Chemistry

Page 2 of 24

1.0e−10

1.0e−11

1.0e−12

1.0e−13

T=7000K T=10000K T=14000K 0

ACS 10Paragon 20Plus Environment 30 40

50 initial vibrational quantum number

60

Page 3 of 24


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

2.5×10−11


1.8e−11 1.6e−11 1.4e−11 1.2e−11 1e−11 8e−12 6e−12 4e−12

2×10−11 1.5×10−11 1×10−11 5×10−12 0 −10 −9 −8 −7 −7 −6 −6 −5 −5 −4 −4 Ev (eV) −3 −3 Ew (eV) −2 −2 −1 −1 0 ACS Paragon Plus Environment 0


3

rate coefficient (cm /s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Page 4 of 24

1.8e−11 1.6e−11 1.4e−11 1.2e−11 1e−11 8e−12 6e−12 4e−12

2.5×10−11 2×10−11 1.5×10−11 1×10−11 5×10−12 0

−7

−6

−5

−4 Ew (eV)−3 −2

−1

0

−9−10 −8 −6−7 −5 Ev (eV) −3−4 −2 0−1

ACS Paragon Plus Environment

Page 1.0e−10 5 of 24

rate coefficient cm3/s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


1.0e−11 1.0e−12 1.0e−13 1.0e−14 1.0e−15

expt.300−730K expt.1200−3000K expt.3000−4500K full QCT quasi−reactive QCT Gordiets’ fit Pavlov’s fit 2000 ACS 4000 Paragon 6000 8000 Plus Environment 12000 temperature (K)

16000

20000


1.0e−10

3000

Page 6 of 24

4000

5000

7000

10000

20000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

The Journal of Physical Chemistry T (K)

this work N+N2 N+N2 Park Ar+N2

1.0e−12 1.0e−14 1.0e−16 1.0e−18 1.0e−20 1.0e−22 1.0e−24 1.0e−26

0.5

ACS1Paragon 1.5Plus Environment 2 2.5 −1

10000/T (K )

3

3.5

Page 7 of 24


original data fit


1 2 3 4 5 10−10 6 7 −12 8 10 9 10 −14 1110 12 60 1310−16 50 14 18000 40 14000 15 30 10000 20 16 6000 10 2000 17 0 ACS Paragon Plus Environment initial v.q.n. 18 temperature (K) 19 20


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 24

Reactive, Inelastic and Dissociation Processes in Collisions of Atomic Oxygen with Molecular Nitrogen F.Esposito*, I.Armenise Consiglio Nazionale delle Ricerche, Nanotec, PLASMI Lab, Via Amendola 122/d, 70126 Bari, Italy Abstract We report the results of detailed calculations of reactive, inelastic and dissociative processes in collisions of atomic oxygen with molecular nitrogen in their respective electronic ground states. Cross sections are calculated as a function of collision energy in the range 0.001-10eV, considering the whole rovibrational ladder. Some problems related to the vibrational energy levels of the asymptotes of 3A” and 3A’ potential energy surfaces used in this work are solved by an appropriate scaling at the level of cross sections. The results are compared with data in the literature, obtaining excellent agreement with experimental thermal data for reactive processes on a very large temperature range, and reasonable agreement with indirect dissociative data. Significant discrepancies are observed with previous reactive state-to-state results calculated on less detailed potential energy surfaces. Inelastic results are compatible with extrapolation of experimental thermal rate coefficient for temperatures higher than 4500K, but completely fail to reproduce experimental data at room temperature. The issue is discussed, indicating the reasons and possible solutions to the problem, and a resonable rate coefficient is obtained combining experimental and theoretical results in the range 300-20000K. Complete, accurate fits are provided for both reactive and dissociative state-to-state rate coefficients in order to use them in applicative numerical codes concerning air kinetics. 1. Introduction The study of air chemical kinetics is fundamental in many applicative fields, such as spacecraft entry into terrestrial atmosphere1,2, electrical discharges3, atmospheric kinetics4, combustion and plasma chemistry in general5,6. It is nowadays well recognized in the literature the importance of vibrational energy exchange in accurately treating these problems (see for example7–10). In fact, molecules can easily exchange vibrational energy by collisions with other atoms and molecules, electrons and radiation, with a strongly enhanced interaction with other species due to nonequilibrium vibrational populations. This interaction can be so relevant that many technological applications are based on plasmas that are "cold" relatively to translation (typically at room temperature), but vibrationally "hot"11. Modeling these conditions can be performed by master equation or direct Monte Carlo (DSMC12) studies coupled to fluidynamics and/or electron kinetics, but the initial problem is of course the availability of vibrationally detailed dynamical data in the form of rate coefficients (for master equation, with a translational equilibrium hypothesis) or of cross sections (for DSMC, without any equilibrium hypotheses on translation, and for this reason computationally more demanding). Concerning air, it is easy to realize that the neutral atomic and molecular species to consider for a consistent kinetics should include N, O, N2, O2 and NO, but as a matter of fact all the molecular species should include vibration, with a much more complex system to consider than the kinetics of the original five species. In fact, N2 has about 61 vibrational levels, O2 about 47 and NO 49. Studies about this topic use input data obtained from many different sources, from simple models of vibrational energy exchange13 and dissociation14 to more or less accurate dynamical calculations performed with a variety of methods15,16. While vibrational energy exchange at low energy can be successfully treated *

[email protected] 1


Page 9 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


with models considering the molecules as simple oscillators, it is easy to realize that for increasing total energies this is insufficient, simply because other effects start taking place, becoming eventually dominating. Considering air species, the most important effect to consider is the reaction, because the atomic species involved have strong mutual attraction, so in a sufficiently energetic collision there is a high probability of formation of unstable compounds that then decay to products with a wide vibrational distribution, because of the strong mixing of different degrees of freedom during the reactive or almost-reactive encounter. This is particularly evident in open-shell atom collisions with diatoms, which for this reason have been studied for decades15,16. Also the present collisional system, O+N2(v), being v the vibrational quantum number, received attention in the past, using quasiclassical17(recently also

18

), semiclassical19 and quantum20

methods. In ref. 17 a study was perfomed about the reaction process with NO formation using the quasiclassical method on two potential energy surfaces (PES) partially developed by the same authors (one PES is from ref.21). However, the product vibrational distribution is only partially available from that study, the results are in the form of rate coefficients (not easily convertible to cross sections22,23), while the PESs used as input of the dynamics can now be considered obsolete, because more accurate treatments by the Sayos group in Barcelona24 have revealed new features and possible reaction paths able to modify the dynamics of vibrational energy exchange, especially sensitive to the PES features. Further new PESs are now available25,26, which confirm the presence of the two C2v minima found by the Barcelona group, and show the presence of a richer structure in both PESs. We think the essential feature that can make the difference with the Bose and Candler PESs is the presence or absence of minima in the strong coupling region, because in our experience (see in particular ref.2) this feature introduces the possibility of a relatively long lasting complex formation that brings to a more statistical final vibrational distribution in products, which is fundamental in the present study focussed on vibration. Moreover, the overall reliability of the Barcelona PESs is further assessed by different studies and comparisons with experiments27–30, including this work. The present study includes not only reaction, but also inelastic processes and dissociation treated with the full vibrational detail, including also initial rotation as a parameter. In the following section the method of calculation is presented with all the details, then in section III the results are subdivided in reactive, inelastic and dissociative processes, including the presentation of analytical fits of rate coefficients for reaction and dissociation with the vibrational detail over a wide temperature range, in order to easily use these results in kinetic codes. Conclusions are then drawn in the last section.

2. Method of calculation The processes considered for calculation in this work are: O+N2(v,j)→N+NO(w,j’=all) reactive channel O+N2(v,j)→O+N2(w,j’=all) inelastic channel O+N2(v,j)→O+N+N dissociation with v/w initial/final vibrational quantum numbers, j/j' initial/final rotational quantum numbers, with atoms and molecules considered in their respective electronic ground states. The dynamics, performed quasiclassically, is calculated adiabatically on the two PESs (3A” ground state, 3A' first excited state, asymptotically degenerate) of ref.24, and then the results are summed by weighting the two contributions with appropriate factors17. Collision energy, considered in the center of mass system, ranges from 1 meV to 10 eV in a continuous way. At the analysis stage, this

2



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 24

range is discretized in 100 bins, but this analysis can be refined if necessary with a finer discretization or with other more efficient methods31,32. Stratified sampling is applied, the maximum interaction distance is 15Å and a uniform density of 5000 trajectories per Å of impact parameter and per eV of collision energy is used in calculations. More than 400 million trajectories were used considering both PESs, with an upper statistical error of about 10-13 cm3/s on state-tostate rate coefficients (once the cross sections are integrated). Every trajectory at each time step is checked by comparing position and velocity with the result of an integration with half the current time step. If the test fails, the time step is further halved, up to a maximum of six times. The check consists in comparing both positions and velocities with a tolerance of 10-9 Å and 10-9 Å/fs respectively. The procedure as a whole is very efficient, because while problematic trajectories are automatically integrated with a very small and expensive time step, the gain on less complex trajectories (with respect to a fix time step able to guarantee similar accuracy) is so relevant that on the average the balance between accuracy and computational requirements is very favorable33. The software used for calculations has been entirely developed in house over the years34, it has been thoroughly tested against accurate quantum mechanical results27,35,36, and specifically adapted for distributed computational grids and highly parallel machines. The collisional system has thousands of possible rovibrational states supported by the asymptotic diatomic potentials of the PESs used. Even if all these states were included in calculations as initial ones, it would be cumbersome to manage all the data in a kinetic code. The approximation adopted here consists in considering as initial states all the vibrational states, but only one in 15 rotational states. Missing data can be recovered from calculated ones with a simple linear interpolation on j for each possibile exit channel (inelastic and reactive ones with final vibration specification, and dissociation). In this way the whole set of cross sections is available starting from “only” about 500 initial states (that is about one tenth of the total number of initial states). The reliability of this procedure has already been discussed in32 at the level of state-selected cross sections, with quite good results. Unfortunately, the diatomic asymptotes of the two PESs used here do not coincide exactly. As a consequence, the two vibrational ladders of N2 and NO are not respectively coincident on the 3A" and 3A’ PESs, in particular for high lying ro-vibrational states. The number of vibrational states on the 3A" for N2 is 61, while on 3A’ is 54, while NO has 53 levels on 3A" but only 52 on 3A’. Of course this is an important problem when using dynamical results in models. The simplest way to overcome this issue consists in using the rate coefficients ignoring the difference in vibrational ladders. This is not recommendable, because the results on the two surfaces should be summed, and this means that on the vibrational ladder an abrupt step in rate coefficient trend is unavoidable, with possible numerical problems in the kinetics. However, the different vibrational ladders cover the same energy interval from diatomic potential minimum to dissociation, so the problem can be overcome by distributing the vibrational results on a different vibrational energy scale by interpolation, considering both reactants and products. For N2 the vibrational scale of reference is taken from the 3A" asymptote (61 levels), which is in accord with the recent literature37,38, as a consequence the 3A' N2 ladder is rescaled to the reference. This is done by linearly interpolating cross sections on initial vibration. Concerning NO, the two ladders from 3A" and 3A’ do not agree with recent determinations38, so they have been both rescaled to the more accurate ladder derived from the diatomic asymptote of N-O-O PES of the same group of Sayos and collaborators39 (49 levels), in order to obtain a consistent set of air species dynamical data usable in modeling. The complete list of levels for each species actually used in this work is reported in supplementary material.

3. Results

3


Page 11 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.1 Thermal reaction rate coefficient Fig.1 reports the thermal reaction rate coefficient for O+N2→NO+N in comparison with some known values in the literature as a function of the inverse of temperature (Arrhenius form). Thermal rate coefficient is obtained here with the appropriate Botzmann sum over the whole ladder of rovibrational states, in the temperature interval 1000-20000K, and compared with the best estimate from the review of Baulch et al.40 obtained using all the experimental data available about this reaction. It is important to stress that the temperature range of experiments for the present reaction in the forward direction is limited between about 1700K and 4000K. In the same figure the direct rate coefficient is shown as obtained from the reverse reaction rate experiments after multiplication by the suited equilibrium constant, taken from the same review. The present results appear in good agreement with the direct data, and almost coincident with the experimental results of the reverse reaction, which were obtained in the temperature range 210-3700K. The quantitative agreement continues also for temperatures quite lower than those shown in fig.1. It is clear that just an extremely small portion of the present cross sections is actually sampled by the translational distribution at low temperature, and as a consequence there is a large amplification of statistical errors. In spite of this, at room temperature the thermal rate coefficient obtained by QCT is higher by no more than a factor 2.3 with respect to the experimental result. At low temperature QCT gives a better result by studying the reverse reaction, because of the better statistics. However, the interest here is in the very good reliability of the rate coefficient slope in the Arrhenius-type graph in a large temperature range.

Fig.1. Thermal reactive rate coefficient for the process O+N2→NO+N in Arrhenius form. Comparison with some theoretical and experimental data from the literature. This global agreement of thermal reaction rate coefficient with experiments is indicative of the very limited relevance of the interaction with the singlet surface of N2O for reaction at high temperatures. For relatively low temperatures, spinorbit transitions to the singlet surface of ground state N2O 41 could modify the present results, if it can be proved that the system has non-negligible probability of switching to the singlet surface and, after some time spent on that PES, returning back to the triplet PESs42. The expected net effect of this double transition would be a wide final vibrational distribution, because the singlet surface would act as a deep well in which the behaviour of the collisional system is more statistical, as in the case of O3 in comparison with N3 (see ref.2 for detailed comments). However this is beyond

4



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 24

the scope of this work. For temperatures higher than those ones of the experiments (about 4000K) the present calculations are well founded, in the sense that the collision energy upper limit of the cross sections calculated in this work guarantee a good reliability up to 15000K at least. Of course, only more extended experimental results can eventually confirm these reasonable computational data, assessing also the possible relevance of special effects at high temperature. In that case one could consider the possible production of excited nitrogen atoms N(2D) on another 3A" surface, not used in this work (see the scheme in ref17). However this should not directly affect the production of N and NO in their respective ground states. The theoretical result by Bose and Candler17 presented in the same figure is significantly lower than both experimental and computational data from this work, while it appears to slowly converge with temperature, up to about 6000K. For higher temperatures the thermal rate runs parallel to the analogous result in this work, with systematically lower values. This discrepancy is reasonably attributable to the remarkable differences in the potential energy surfaces adopted in the two calculations. As noted in 24,27, there is a C2v minimum in both surfaces of Sayos and collaborators, while this feature is completely absent in the Bose and Candler surfaces. These features are confirmed also in a recently published paper by other authors25. In the same figure also an extrapolation of the Bose and Candler data to lower temperatures is presented, in order to show the quite different, more negative slope of the Arrhenius-type graph, with a discrepancy of two orders of magnitude at 1000K, not reported in the figure. This is an important difference to be taken into account in applicative models, where often data are tentatively extrapolated from their original ranges. This different slope with respect to present calculations continues also for high temperatures. The present calculated thermal rate coefficient can be accurately reproduced using this Arrhenius fit: Rreact(T) = 1.2686*10-13 T-0.874 exp(-36899/T) cm3/s 3.2 State-to-state reactive rate coefficients Some of our state-to-state cross sections received some accurate confirmations with wave packet calculations in

27

and

43

with quasiclassical calculations in an independent work (see fig.3 of ref. ). The lower values of reaction rate coefficients for the Bose-Candler set of results with respect to the present ones are confirmed with more details in the state-to-state rate coefficient comparison in fig.2, where they are represented as a function of initial vibrational quantum number v at three ro-translational temperature values, T=7000K (red), T=10000K (green), T=14000K (blue). The difference between the two sets increases for increasing v, therefore an extrapolation on vibration of the Bose-Candler data can be significantly different at any temperature. As detailed in section II, vibrational state-to-state cross sections, suitable as input of Direct Monte Carlo codes, cover the whole vibrational ladders of reactants and products in this work, including also initial rotation, for collision energies up to 10 eV. These data are available upon request from the authors. The accuracy of some samples of these cross sections is discussed in ref.27, with quite good results concerning the comparison with quantum mechanical time dependent calculations. However, in many kinetic models with translational equilibrium a compact way of providing these results can be very useful and much easier to manipulate. In the present work this operation consists in fitting the rate coefficient data to a multivariate polynomial by the linear least square method. The interpolation is performed as a function of ro-translational temperature and of the N2 and NO vibrational energies (indicated as Ev and Ew, respectively), rather than as a function of their vibrational levels, v and w, in order to prevent re-scaling problems. In fact, it is quite common to find in the literature input data for different processes including the same molecule (e.g. N2 from VT of N+N2 and O+N2) with different vibrational ladders44.

5


Page 13 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig.2. Reaction rate coefficients as a function of initial vibrational states for some values of ro-translational temperature, T=7000K (red crosses), T=10000K (green “x”), T=14000K (blue stars). The curves obtained in this work are indicated with full lines, while Bose and Candler results appear with dotted lines. The origins of the vibrational energy values can be quite heterogeneous, from simple models to experimental data limited to relatively low lying states, or from slightly different asymptotic diatomic curves obtained from different PESs. In a kinetic simulation it is necessary to set only one vibrational ladder for each molecular species, so once it has been chosen, a rescaling of all the different ladders of the same species must be done. If the rate coefficient interpolation is performed on energy values rather than on quantum numbers, then the scaling is really straightforward44. Moreover, v>w for the present system does not necessarily imply exothermicity, as in the case of symmetric systems (e.g. VT rate coefficients of N+N2

45

, O+O2

46

), because the w=0 of NO has an energy

approximately equal to v=12 of N2. As a consequence, the rate coefficient as a function of v for a fixed final w1 is endothermic up to a v1 value such that Ev1v’=0 is shown. The result obtained in this work by the QCT method is represented by the green curve with "x", with the label "full QCT". The rotational temperature is equal to the translational one, while final rotation is summed. A non-negligible rate coefficient can be appreciated only starting from temperatures higher than 2000K, with a steep increase as a function of temperature, and a value of 1.1*10-11 cm3/s at T=10000K. In the same figure the experimental results by McNeal et al.47 in the range 300-730K, Eckstrom48 in the range 1200-3000K, and Breshears and Bird49 (3000-4500K) are shown. Unfortunately experimental results are unavailable for temperatures higher than 4500K. The original experimental data consist of pτv evaluations (with p pressure, τv vibrational relaxation time), while the inelastic deexcitation rate coefficient K10 from v=1 (with energy E1) to v'=0 (with energy E0) is obtained here by means of the relation: K10 = kT/{pτv[1-exp(-(E1-E0)/kT)]}

(2)

This is based on the Bethe-Teller model for vibrational energy exchange50, which relies upon the hypothesis of a forced harmonic oscillator for the molecular vibrator in interaction with the impinging atom. In the same figure two curve fits based on the experimental findings are shown. The fit by Pavlov51 is obtained in the range 300-3000K, and it is based on a Landau-Teller formula with a T-1/3 dependence. It appears to be perfectly adequate up to 3000K. For higher temperatures, the experimental points of Breshears and Bird, not considered in the Pavlov's fit, appear somewhat higher and with a steeper trend than the extrapolation of the fit. On the contrary, the Gordiets' fit16 includes also the Breshears and Bird data at T>3000K, and the shape of the curve is significantly different from the Landau-Teller curve, in fact it is modeled as a double Arrhenius curve, with a steeper trend starting from about 2500K. This is relevant for this discussion, in that it suggests the possibility of presence of different mechanisms for vibrational deactivation, as also stressed by Gordiets et al.16. The low temperature rate coefficient is dominated by the Landau-Teller mechanism, as also the low temperature fit suggests. However, when temperature increases, other mechanisms start contributing. It is clear from the comparison that QCT calculations give a result quite high and continuously increasing for temperatures higher than about 6000K. To better investigate this point, we have separated the QCT result into a "purely non-reactive" (PNR,

8



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 24

not shown) contribution and a "quasi-reactive" (QR)52 (or "recrossing"53,54) contribution (shown in the figure).

fig.4. Non-reactive vibrational deexcitation rate coefficient from v=1 as obtained in this work (QCT labels, solid curves with markers), in comparison with some experimental results (markers) and fits (dots and dashes). See text for the difference between full QCT and quasi-reactive QCT. The PNR condition is obtained in a trajectory if no one of the two internuclear distances between the impinging O atom and the two N atoms in the molecule becomes lower than the N-N bond. A slightly refined version is applied here52, consisting in evaluating the same condition for the ratios of each distance with the equilibrium distance of the respective isolated diatom (N2, NO). If the PNR condition is false, then an inelastic event is classified as QR. In this case, the atomic projectile enters the strong coupling region, and its interaction is strong due to the attractive forces with the atomic species in the molecule. This interaction, which cannot be modeled with a forced harmonic oscillator50,55, is the same that is present in reactive events, with a weakening or temporary breaking of the original molecular bond during the event. Even if the final outcome is in the inelastic channel, the dynamics is completely different from a PNR interaction32,54. In fact, QR events require sufficient energy to overcome the barrier to reaction, and the final vibrational distribution is generally flat and wide (contrarily to the typical highly peaked PNR distribution56), because of the strong mixing of vibrational and translational energy during the interaction. The presence of a threshold is clear in the QR QCT result in the figure, and it is completely justified by the QR mechanism. However, the full QCT result is practically coincindent with the QR result at low temperature. This is due to a failure of the quasiclassical method with binning when the vibrational energy exchanged in a PNR event is so low that the final vibrational outcome differs from the initial vibration less than half a quantum. In this case, the outcome erroneously appears as an elastic contribution only. When the collision energy increases, also the PNR vibrational distribution becomes wide, and an accurate result can generally be gained. This means that at sufficiently high temperature also the PNR QCT result becomes reliable. A more accurate analysis of these QCT results will be the topic of a specific work, including also comparisons with other dynamical methods. It is important to realize that quasi-reactive trajectories have essentially the same behaviour as reactive ones, and their contribution can be considered accurate if the reactive events are correctly treated. As already shown, the reactive part is in quantitative agreement with experiments and has a reasonable high energy trend, as a consequence the corresponding high energy QR inelastic part can be considered reliable to the same extent (differently from the low energy PNR contribution, which strongly depends on the entrance channel long range features of the PES, as well known).

9


Page 17 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Summarizing, the QCT inelastic rate coefficient includes different components, whose reliability is different. While the PNR contribution has some problems at low energy, and gradually becomes reliable for increasing temperatures, the QR part has essentially the same reliability of the reactive part, which in this work is quite good. It is noteworthy that the steep slope of the QR QCT rate coefficient is very similar to that of the Breshears and Bird experimental result, even if its values are quite lower. The QR contribution starts to be non-negligible at the temperatures of the experiment, while it is surely relevant at high temperature. However, a third component should be considered and added to obtain the complete inelastic rate coefficient, originating from a strong three-body interaction on the singlet, attractive PES of N2O, which could be accessible by an intersystem crossing from the triplet PESs used in this work. This contribution can be relevant at intermediate temperatures (including the range of the Breshears and Bird experiment), because the intersection of triplet with singlet PESs takes place at an energy value not lower than 1eV42,57. For higher energy this mechanism is less efficient and probably could be neglected. As a consequence, three mechanisms appear to be in action at different energies: the Landau-Teller mechanism (a PNR one) especially relevant at low temperature, an intersystem crossing contribution in the intermediate range, and a QR mechanism at high temperature. A non-reactive quantum mechanical method is advisable for the first contribution (as in20, where a different PES was used), a nonadiabatic method is needed for the second one (couplings between triplet and singlet surfaces are also necessary, as in ref.57), whereas the QR contribution is given in this work by means of QCT. Considering that two components are still missing, the inelastic rate coefficients obtained in this work, which cover the whole rovibrational ladder as in the reactive case, are not given in a compact form by using surface fitting. The approximation that could be formulated on the basis of this work and the current knowledge is to consider the inelastic deexcitation rate coefficient from v=1 in O+N2 collisions as the maximum of both the experimental fit of Gordiets and the present inelastic result. This is because the full QCT result for T>=10000K has both reliable PNR and QR components, as previously discussed. Of course, this is only a first approximation, because the intermediate range between 4500K and 10000K is just an extrapolation, and it concerns only the first N2 vibrational state. 3.4 Thermal dissociation rate coefficient Direct experimental dissociation data about O+N2 collisions are not available, so many authors have proposed different combinations of atomic species that should behave “similarly” to the current system. Of course this means that a comparison with experiments will remain uncertain until direct data are obtained. In fig.5 the thermal rate coefficient for dissociation from this work as a function of 10000/T is shown in comparison with data from the Russian AVOGADRO database of experimental origin58,59, where O+N2 dissociation is considered to be approximately equal to N+N2 dissociation. Another source of N+N2 dissociation is the Park's data60 represented in the figure, which show a slightly lower slope with respect to all the other results. Finally Dunn and Kang61 results are shown, relative to Ar+N2 dissociation, taken in the past as representative of N2 dissociation in collision with atoms, in absence of other data.

10



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 24

Fig.5. Thermal dissociation rate coefficient as a function of 10000/T (K-1) (Arrhenius plot), as obtained in this work for O+N2 collisions and from experiments for Ar+N2 and N+N2 collisions. It is interesting to note that the Dunn and Kang results61 are systematically lower, while N+N2 appear systematically higher than O+N2 dissociation. The first observation is reasonable, because N2 dissociation originated from a noble gas collision is less efficient than the one from an atomic species attractive with respect to N. In fact, in presence of repulsive interaction alone, the molecule can only be compressed by the impinging atom, with subsequent dissociation. On the contrary, collisions with attractive species are more likely to produce dissociation, because in this case even a stretching is able to contribute62. In this sense it is also reasonable that N+N2 dissociation is higher than O+N2 one, being N2 more tightly bound than NO. The possibility of reaction means that in the strong coupling region the original molecular bond is weakened by the presence of the third attractive body, so its breaking in a dissociative event is more likely. This is confirmed in ref.62, which show a direct correlation between reliable quasiclassical dissociation and the presence of both reactive and unreactive channels. In the case of this work, the reaction threshold is about 3.3 eV above the reactants ground state, but the dissociation channel opens for total energies higher than 9.91eV, when reaction and inelastic channels are reliably obtained with QCT, so the quasiclassical "direct" three-body dissociation should be reliable for this system. The possibility of an "indirect" dissociation means that there is first a collision with atoms with the formation of a rotational quasibound state, which can then dissociate if its lifetime is smaller than the mean collision time (ORT mechanism63). This treatment of dissociation could be added to direct three-body dissociation (see63 for important details). However this mechanism, while very important for light species as hydrogen and helium at low temperature, should have minor relevance for air molecular species because of the heavier masses, which means lower probabilities of traversing the quasibound rotational barrier. This observation is supported also by the small fraction of N2 quasibound states with lifetimes lower than picoseconds (about 8%, calculated in this work by WKB approximation64 on the present N2 vibrational scale, see supplementary material), in comparison for example with molecular hydrogen (about 40%, see63). Another aspect that should be considered for O+N2 dissociation is the fact that three PESs are degenerate in the reactants (see fig.1 of ref.17). Two of them are considered in this work (3A” and 3A’ correlating with ground state NO(X2∏) and N(4S)), but there is also another 3A” correlating with excited 2D atomic nitrogen (this is the origin of the 1/3 factor). Commonly dissociation experiments do not distinguish final atomic state, as a consequence for the present collisional system it would be more correct to include also dissociation into excited

11


Page 19 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


atomic nitrogen, using the appropriate PES. In absence of this contribution, one could approximate the N(2D) dissociation channel by taking the average dissociation value calculated on the ground state 3A” and 3A’ from this work. It is easy to show that this means to substitute the 1/3 factor applied to the calculations on each PES with ½. The thermal dissociation rate coefficient would remain within the same lower and upper limits of Ar+N2 and N+N2 results. Due to the lack of experimental data for comparison about the specific system treated here, we avoided to consider in an approximate way the presence of stable N2 excited electronic states using the Nikitin model65, as we did for the O+O2 dissociation case in ref.33. However, it is quite easy to add the model to the present data, see the cited references for details. The present result (considering 1/3 factor and without the Nikitin model) can be accurately reproduced by means of the following Arrhenius fit: Rdiss(T) = 1.206*10-8 T0.926 exp(-11.713/T) cm3/s

fig.6. Dissociation state-selected rate coefficients as a function of initial vibrational quantum number and rotranslational temperature. 3.5 State-selected dissociation rate coefficients The state-selected dissociation rate coefficients are presented in fig.6 as a function of temperature T and initial vibrational quantum number v. As can be easily seen, at low T the increase of dissociation is extremely rapid with v, with negligible values for low-lying vibrational states. At high temperature also the lowest vibrational states contribute not negligibly to dissociation and the slope with v is much lower. Also state-selected dissociation rate coefficients are available in a surface fitting, obtained in this work similarly to the VT case, using the following multivariate polynomial as a function of v and T:

!

𝑅!!"# 𝐸! , 𝑇 = * 𝑒𝑥𝑝

! !!! 𝑑!

!

𝐸! ∗

! !

(3)

!

with

𝑑! 𝐸!

=

! !!! 𝑧!" ∗

𝐸!

!

+ 𝑧!! ∗

! !!

12



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 24

A complete Fortran code of the interpolation in eq.3 is available in supplementary material. The degeneracy factor 1/3 is explicitly indicated for the reasons already explained for the thermal rate coefficient. Only values larger than 10-30 cm3/s are considered in the fit, for the same considerations relative to the reactive processes. The fit mean relative error is equal to 6%, calculated for rates greater than 10-20 cm3/s. The accuracy of the fit can also be appreciated from the comparison in fig.6, where the original data are shown with markers, whereas lines represent the fit. Dissociation and VT rate coefficients from this work could be obtained also with a rotational temperature different from the translational one, but for practical reasons their surface fits include only a ro-translational temperature. 4. Conclusions In this paper the collisions of atomic oxygen with molecular nitrogen in their respective ground states are treated quasiclassically, obtaining vibrational state-to-state cross sections for reactive, inelastic and dissociation processes on the full vibrational ladders of reactants and products. The thermally averaged result for reaction is compared with the recommended experimental data, with very good agreement in the full range of available data. The thermal dissociation rate coefficient is in reasonable agreement with data from collisions of similar species, being the appropriate experimental result missing. For both processes the vibrationally detailed results are accurately interpolated in order to use the data in kinetic codes. On the other side, from the comparison of the inelastic rate coefficient for deexcitation from v=1 with available experimental fits, it is clear that some problems should be solved concerning the dynamical treatment of the collision. In fact, while the extrapolation of experimental data at high temperature is compatible with quasiclassical results, the room temperature rate coefficient is higher by many orders of magnitude. The issue is studied by separating the QCT result into purely non-reactive and quasi-reactive trajectories, i.e. inelastic trajectories that respectively avoid or enter the strong coupling region. This allows understanding that the apparent threshold in deexcitation is essentially due to quasi-reactive events, which correctly show a threshold behaviour, while the purely non-reactive contribution is practically zero at low energy, due to the binning issues in QCT at low temperature. On the contrary it is clear that for high temperatures the purely non-reactive contribution is quite high, so the complete QCT result can be considered reliable. As a consequence, the extrapolation of the Gordiets' fit to deexcitation should be increased for T>10000K up to the QCT result. In the intermediate range it remains to be assessed the relevance of interaction with the singlet surface of N2O. In conclusion, the present inelastic result is only a partial one. To reproduce the low temperature experimental data and extend it to other low lying vibrational states other approaches different from QCT with binning are needed, and some work in this direction is under way. Supporting Information In supplementary material we report: 1) the complete list of vibrational levels (at j=0) for N2 and NO species actually used in this work. 2) Fortran code of rate coefficient interpolation concerning reaction and dissociation processes. 3) list of lifetimes of quasibound states of N2, as obtained from the diatomic asymptote of the 3A" PES used in this work. Acknowledgment

13


Page 21 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The computational time was supplied by CINECA (Bologna) under ISCRA project N. HP10CXWOPW References

(1) Capitelli, M.; Celiberto, R.; Colonna, G.; D’Ammando, G.; De Pascale, O.; Diomede, P.; Esposito, F.; Gorse, C.; Laricchiuta, A.; Longo, S.; et al. Plasma Kinetics in Molecular Plasmas and Modeling of Reentry Plasmas. Plasma Phys. Control. Fusion 2011, 53, 124007. (2) Celiberto, R.; Armenise, I.; Cacciatore, M.; Capitelli, M.; Esposito, F.; Gamallo, P.; Janev, R. K.; Laganà, A.; Laporta, V.; Laricchiuta, A.; et al. Atomic and Molecular Data for Spacecraft Re-Entry Plasmas. Plasma Sources Sci. Technol. 2016, 25 (3), 33004. (3) Pintassilgo, C. D.; Guerra, V. Modelling of the Temporal Evolution of the Gas Temperature in N2 Discharges. Plasma Sources Sci. Technol. 2017, 26 (5), 55001. (4) Yankovsky, V.; Manuilova, R.; Babaev, A.; Feofilov, A.; Kutepov, A. Model of ElectronicVibrational Kinetics of the O3 and O2 Photolysis Products in the Middle Atmosphere: Applications to Water Vapour Retrievals from SABER/TIMED 6.3 µm Radiance Measurements. Int. J. Remote Sens. 2011, 32 (11), 3065–3078. (5) Capitelli, M.; Celiberto, R.; Esposito, F.; Laricchiuta, A. Molecular Dynamics for State-toState Kinetics of Non-Equilibrium Molecular Plasmas: State of Art and Perspectives. Plasma Process. Polym. 2009, 6 (5), 279–294. (6) Capitelli, M.; Celiberto, R.; Colonna, G.; Esposito, F.; Gorse, C.; Hassouni, K.; Laricchiuta, A.; Longo, S. Fundamental Aspects of Plasma Chemical Physics; Springer Series on Atomic, Optical, and Plasma Physics; Springer New York: New York, NY, 2016; Vol. 85. (7) Hurlbatt, A.; Gibson, A. R.; Schröter, S.; Bredin, J.; Foote, A. P. S.; Grondein, P.; O’Connell, D.; Gans, T. Concepts, Capabilities, and Limitations of Global Models: A Review. Plasma Process. Polym. 2017, 14 (1–2), 1600138–n/a. (8) Pintassilgo, C. D.; Guerra, V. Power Transfer to Gas Heating in Pure N2 and in N2 –O2 Plasmas. J. Phys. Chem. C 2016, 120 (38), 21184–21201. (9) Capitelli, M.; Armenise, I.; Bisceglie, E.; Bruno, D.; Celiberto, R.; Colonna, G.; D’Ammando, G.; De Pascale, O.; Esposito, F.; Gorse, C.; et al. Thermodynamics, Transport and Kinetics of Equilibrium and Non-Equilibrium Plasmas: A State-to-State Approach. Plasma Chem. Plasma Process. 2012, 32 (3), 427–450. (10) Nagnibeda, E.; Kustova, E. Non-Equilibrium Reacting Gas Flows; Heat and Mass Transfer; Springer Berlin Heidelberg: Berlin, Heidelberg, 2009. (11) Taccogna, F.; Dilecce, G. Non-Equilibrium in Low-Temperature Plasmas. Eur. Phys. J. D 2016, 70 (11). (12) Bruno, D.; Capitelli, M.; Esposito, F.; Longo, S.; Minelli, P. Direct Simulation of NonEquilibrium Kinetics under Shock Conditions in Nitrogen. Chem. Phys. Lett. 2002, 360 (1–2), 31– 37. (13) Dmitrieva, I. K.; Zenevich, V. A. Effect of the Vibrational Nitrogen Excitation on the Rate Constant of the N2(v) + O → NO + N: A Theoretical–Information Approximation. Khim Fiz 1984, 3 (8), 1075–1080. (14) Wysong, I.; Gimelshein, S.; Gimelshein, N.; McKeon, W.; Esposito, F. Reaction Cross Sections for Two Direct Simulation Monte Carlo Models: Accuracy and Sensitivity Analysis. Phys. Fluids 2012, 24 (4), 42002. (15) Capitelli, M. Nonequilibrium Vibrational Kinetics; Topics in Current Physics; SpringerVerlag, 1986; Vol. 39. (16) Capitelli, M.; Ferreira, C. M.; Gordiets, B.; Osipov, A. I. Plasma Kinetics in Atmospheric Gases; Atomic, Optical and Plasma Physics; Springer Berlin / Heidelberg, 2000. (17) Bose, D.; Candler, G. V. Thermal Rate Constants of the N2+O->NO+N Reaction Using Ab Initio 3A" and 3A’ Potential Energy Surfaces. J. Chem. Phys. 1996, 104, 2825. (18) Lin, W.; Meana-Pañeda, R.; Varga, Z.; Truhlar, D. G. A Quasiclassical Trajectory Study of 14



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 24

the N2(X1Σ) + O(3P) → NO(X2Π) + N(4S) Reaction. J. Chem. Phys. 2016, 144 (23), 234314. (19) Balakrishnan, N.; Dalgarno, A. Nitric Oxide Production in Collisions of Hot O(3P) Atoms with N2. J Geophys Res 2003, 108 (A2), 1065. Despite the semiclassical method used in that work, which is expected to be more accurate than the quasiclassical trajectory method, we didn't consider results from that paper because they appear to be affected by some problems with the reaction thresholds. (20) Ivanov, M. V.; Schinke, R.; Mcbane, G. C. Theoretical Investigation of Vibrational Relaxation of NO(2Π ), O2, and N2 in Collisions with O(3P). Mol. Phys. 2007, 105, 1183–1191. (21) Gilibert, M.; Aguilar, A.; González, M.; Mota, F.; Sayós, R. Dynamics of the N(4Su) + NO(X2Π) → N2(X1Σg+) + O(3Pg) Atmospheric Reaction on the 3A‘ Ground Potential Energy Surface. I. Analytical Potential Energy Surface and Preliminary Quasiclassical Trajectory Calculations. J. Chem. Phys. 1992, 97 (8), 5542–5553. (22) Minelli, P.; Esposito, F.; Bruno, D.; Capitelli, M.; Longo, S. Extracting Cross Sections from Rate Coefficients: Application to Molecular Gas Dissociation. J.Ther.Heat.Transf. 2011, 25, 374. (23) Baykov, B. S.; Bayalina, D. K.; Kustova, E. V. Inverse Laplace Transformation for Evaluation of State-Specific Cross Sections for Dissociation Reaction and Vibrational Energy Transitions. Vestn. St Petersburg Univ. Math. 2016, 49 (4), 389–397. (24) Gamallo, P.; González, M.; Sayós, R. Ab Initio Study of the Two Lowest Triplet Potential Energy Surfaces Involved in the N(4S)+NO(X  2Π) Reaction. J. Chem. Phys. 2003, 118, 10602. (25) Lin, W.; Varga, Z.; Song, G.; Paukku, Y.; Truhlar, D. G. Global Triplet Potential Energy Surfaces for the N2(X1Σ) + O(3P) → NO(X2Π) + N(4S) Reaction. J. Chem. Phys. 2016, 144 (2), 24309. (26) Denis-Alpizar, O.; Bemish, R. J.; Meuwly, M. Reactive Collisions for NO( 2∏) + N( 4 S) at Temperatures Relevant to the Hypersonic Flight Regime. Phys Chem Chem Phys 2017, 19 (3), 2392–2401. (27) Akpinar, S.; Armenise, I.; Defazio, P.; Esposito, F.; Gamallo, P.; Petrongolo, C.; Sayós, R. Quantum Mechanical and Quasiclassical Born–Oppenheimer Dynamics of the Reaction N2+O→N+NO on the N2O a3A" and b3A’ Surfaces. Chem. Phys. 2012, 398, 81–89. (28) Jorfi, M.; Honvault, P. State-to-State Quantum Reactive Scattering Calculations and Rate Constant for Nitrogen Atoms in Collision with NO Radicals at Low Temperatures. J. Phys. Chem. A 2009, 113 (40), 10648–10651. (29) Gamallo, P.; Sayós, R.; González, M.; Petrongolo, C.; Defazio, P. Quantum Real WavePacket Dynamics of the N(4S)+NO(X̃ 2Π)→N2(X̃ 1Σg+)+O(3P) Reaction on the Ground and First Excited Triplet Potential Energy Surfaces: Rate Constants, Cross Sections, and Product Distributions. J. Chem. Phys. 2006, 124 (17), 174303. (30) Defazio, P.; Gamallo, P.; González, M.; Akpinar, S.; Bussery-Honvault, B.; Honvault, P.; Petrongolo, C. Quantum Dynamics of the C(1D)+HD and C(1D)+n−D2 Reactions on the Ã  1Aʹ and B̃  1A" surfaces. J. Chem. Phys. 2010, 132 (10), 104306. (31) Aoiz, F. J.; Luis Bañares; Herrero, V. J. Recent Results from Quasiclassical Trajectory Computations of Elementary Chemical Reactions. J Chem Soc Faraday Trans 1998, 94 (17), 2483– 2500. (32) Capitelli, M.; Celiberto, R.; Colonna, G.; Esposito, F.; Gorse, C.; Hassouni, K.; Laricchiuta, A.; Longo, S. Reactivity and Relaxation of Vibrationally/Rotationally Excited Molecules with Open Shell Atoms. In Fundamental Aspects of Plasma Chemical Physics; Springer Series on Atomic, Optical, and Plasma Physics; Springer New York, 2016; Vol. 85, pp 31–56. (33) Esposito, F.; Capitelli, M. Quasiclassical Trajectory Calculations of Vibrationally Specific Dissociation Cross-Sections and Rate Constants for the Reaction O+O2(v)-> 3O. Chem.Phys.Lett. 2002, 364, 180–187. (34) Esposito, F. Dinamica Quasiclassica Di Processi Collisionali Inelastici E Reattivi in Sistemi H+H2 E N+N2 Rotovibrazionalmente Risolti. PhD Thesis, Università degli Studi di Bari: Bari, 15


Page 23 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1999. (35) De Fazio, D. The H+HeH+ → He+H2+ Reaction from the Ultra-Cold Regime to the ThreeBody Breakup: Exact Quantum Mechanical Integral Cross Sections and Rate Constants. Phys Chem Chem Phys 2014, 16 (23), 11662–11672. (36) Esposito, F.; Coppola, C. M.; De Fazio, D. Complementarity between Quantum and Classical Mechanics in Chemical Modeling. The H + HeH+ → H2+ + He Reaction: A Rigourous Test for Reaction Dynamics Methods. J. Phys. Chem. A 2015, 119, 12615−12626. (37) Le Roy, R. J.; Huang, Y.; Jary, C. An Accurate Analytic Potential Function for GroundState N2 from a Direct-Potential-Fit Analysis of Spectroscopic Data. J. Chem. Phys. 2006, 125, 164310. (38) Lino da Silva, M.; Guerra, V.; Loureiro, J.; Sá, P. A. Vibrational Distributions in N2 with an Improved Calculation of Energy Levels Using the RKR Method. Chem. Phys. 2008, 348 (1–3), 187–194. (39) Sayós, R.; Oliva, C.; González, M. New Analytical (2Aʹ,4A’) Surfaces and Theoretical Rate Constants for the N(4S)+O2 Reaction. J. Chem. Phys. 2002, 117, 670. (40) Baulch, D. L.; Bowman, C. T.; Cobos, C. J.; Cox, R. A.; Just, T.; Kerr, J. A.; Pilling, M. J.; Stocker, D.; Troe, J.; Tsang, W.; et al. Evaluated Kinetic Data for Combustion Modeling: Supplement II. J. Phys. Chem. Ref. Data 2005, 34 (3), 757–1397. (41) Macheret, S. O.; Rusanov, A.; Friedman, G. V. Nonequilibrium Plasma-Chemical Process of Synthesis of Nitrogen Oxide Emissions. J. Tech. Phys. 1980, 50, 705. (42) Fisher, E. R.; Bauer, E. On the Quenching of O(1D) by N2 and Related Reactions. J. Chem. Phys. 1972, 57 (5), 1966. (43) Luo, H.; Kulakhmetov, M.; Alexeenko, A. Ab Initio State-Specific N2 + O Dissociation and Exchange Modeling for Molecular Simulations. J. Chem. Phys. 2017, 146 (7), 74303. (44) Armenise, I.; Esposito, F. N2, O2, NO State-to-State Vibrational Kinetics in Hypersonic Boundary Layers: The Problem of Rescaling Rate Coefficients to Uniform Vibrational Ladders. Chem. Phys. 2015, 446, 30–46. (45) Esposito, F.; Armenise, I.; Capitelli, M. N-N2 State to State Vibrational-Relaxation and Dissociation Rates Based on Quasiclassical Calculations. Chem. Phys. 2006, 331 (1), 1–8. (46) Esposito, F.; Armenise, I.; Capitta, G.; Capitelli, M. O-O2 State-to-State Vibrational Relaxation and Dissociation Rates Based on Quasiclassical Calculations. Chem. Phys. 2008, 351 (1–3), 91–98. (47) McNeal, R. J.; Whitson Jr., M. E.; Cook, G. R. Quenching of Vibrationally Excited N2 by Atomic Oxygen. Chem. Phys. Lett. 1972, 16 (3), 507–510. (48) Eckstrom, D. J. Vibrational Relaxation of Shock-Heated N2 by Atomic Oxygen Using the Ir Tracer Method. J. Chem. Phys. 1973, 59 (6), 2787. (49) Breshears, W. D.; Bird, P. F. Effect of Oxygen Atoms on the Vibrational Relaxation of Nitrogen. J. Chem. Phys. 1968, 48 (10), 4768. (50) H. A. Bethe; E. Teller. Deviations from Thermal Equilibrium in Shock Waves; X-117; Ballistic Research Labs, 1941. (51) Pavlov, A. V. Vibrationally Excited N2 and O2 in the Upper Atmosphere: A Review. Geomagn. Aeron. 2011, 51, 143–169. (52) Smith, I. W. Reaction and Relaxation of Vibrationally Excited Molecules: A Classical Trajectory Study of Br+HCl(v′) and Br+DCl(v′) Collisions. Chem. Phys. 1977, 20 (3), 437–443. (53) Aoiz, F. J.; Bañares, L.; Herrero, V. J. The H+H2 Reactive System. Progress in the Study of the Dynamics of the Simplest Reaction. Int. Rev. Phys. Chem. 2005, 24 (1), 119–190. (54) Greaves, S. J.; Wrede, E.; Goldberg, N. T.; Zhang, J.; Miller, D. J.; Zare, R. N. Vibrational Excitation through Tug-of-War Inelastic Collisions. Nature 2008, 454 (7200), 88–91. (55) Treanor, C. E. Vibrational Energy Transfer in High-Energy Collisions. J. Chem. Phys. 1965, 43 (2), 532. 16



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 24

(56) Nikitin, E. E.; Troe, J. 70 Years of Landau–Teller Theory for Collisional Energy Transfer. Semiclassical Three-Dimensional Generalizations of the Classical Collinear Model. Phys. Chem. Chem. Phys. 2008, 10 (11), 1483. (57) Nakamura, H.; Kato, S. Theoretical Study on the Spin-Forbidden Predissociation Reaction of N2O: Ab Initio Potential Energy Surfaces and Quantum Dynamics Calculations. J. Chem. Phys. 1999, 110 (20), 9937. (58) Losev, S. A.; Makarov, V. N.; Pogosbekyan, M. Y. Model of the Physico-Chemical Kinetics behind the Front of a Very Intense Shock Wave in Air. Fluid Dyn. 1995, 30 (2), 299–309. (59) Krivonosova, O.; Losev, S.; Nalivaiko, V.; Mukoseev, Y. K.; Shatalov, O. Recommended Data on the Rate Constants of Chemical Reactions between Molecules Consisting of N and O Atoms. Plasma Chem. 1987, 14, 3–31. (60) Park, C. A Review of Reaction Rates in High Temperature Air. AIAA Pap. 1989, No. 89– 1740. (61) Dunn, M. G.; Kang, S. W. Theoretical and Experimental Studies of Re-Entry Plasmas; NASA CR 2232; 1973. (62) Dove, J. E.; Mandy, M. E.; Sathyamurthy, N.; Joseph, T. On the Origin of the Dynamical Threshold for Collision-Induced Dissociation Processes. Chem. Phys. Lett. 1986, 127 (1), 1–6. (63) Esposito, F.; Capitelli, M. Selective Vibrational Pumping of Molecular Hydrogen via Gas Phase Atomic Recombination. J. Phys. Chem. A 2009, 113, 15307–15314. (64) Kuntz, P. J. Collision-Induced Dissociation II: Trajectories and Models. In Atom-Molecule Collision Theory: A Guide for the Experimentalist; 1979. (65) Nikitin, E.E. Theory of Elementary Atomic and Molecular Processes in Gases; Clarendon Press: Oxford, 1974.

17


Reactive, Inelastic, and Dissociation Processes in Collisions of Atomic

Recommend Documents